Abstract
We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian maximum a posteriori estimators. Our scheme takes the form of a convex alternating minimization, over the trajectories and the dynamic model respectively. We prove its convergence to a local minimum which verifies a two point-boundary problem for the (latent) state variable and a tensor product expression for the optimal dynamics.
| Original language | English |
|---|---|
| Article number | 34 |
| Pages (from-to) | 1-10 |
| Journal | Communications in Optimization Theory |
| Volume | 2023 |
| DOIs | |
| Publication status | Published - 10 Jul 2023 |
Bibliographical note
Publisher Copyright:© 2023 Communications in Optimization Theory.
Funding
The first author was funded by the European Research Council (grant REAL 947908). The second author was supported by the National Science Foundation under grants NSF-DMS1905449, NSF-DMS-2204795 and grant from the SAR Hong Kong RGC GRF 14301321. The third author acknowledges partial financial support for this work from a General Research Fund by the Research Grants Council (RGC) of Hong Kong SAR, China (Project No. 11303421), a grant from ITF- Guangdong-Hong Kong Technology Cooperation Funding Scheme (Project Ref. No. GHP/145/20), and a Math and Application Project (2021YFA1003504) under the National Key R&D Program.
Keywords
- Alternating minimization
- Continuous-time linear dynamic system
- Latent variable
- System identification
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